025-fancy-indexing.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Advanced Indexing (Fancy Indexing)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([12, 34, 56, 78, 90])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([12, 34, 56, 78, 90])\n",
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Advanced Indexing: Integers\n",
    "Advanced inexing can be triggered by using a list or an array while idexing:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([12, 78, 90])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[[0, 3, 4]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([12, 78, 90])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# the same:\n",
    "take = [0, 3, 4]\n",
    "a[take]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([12, 78, 90])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "take = np.array([0, 3, 4])\n",
    "a[take]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The same index value can bu used more than once, to construct a new array in the same shape as the supplied list:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([12, 34, 12, 56])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[[0, 1, 0, 2]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(12,)\n",
      "[56 12 34 12 34 34 34 34 12 56 12 90]\n",
      "(12,)\n"
     ]
    }
   ],
   "source": [
    "take = np.array([2, 0, 1, 0, 1, 1, 1, 1, 0, 2, 0, 4])\n",
    "print(take.shape)\n",
    "print(a[take])\n",
    "print(a[take].shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This works with multidimensional arrays as well!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[12, 34, 12],\n",
       "       [34, 56, 34],\n",
       "       [12, 34, 12]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "take2 = np.array([\n",
    "    [0, 1, 0], \n",
    "    [1, 2, 1], \n",
    "    [0, 1, 0],\n",
    "])\n",
    "a[take2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note: the examples above used a 1-d list or an array to trigger advanced indexing.\n",
    "Advanced indxing can be triggered even with a tuple for any axis containing a sequence:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[12, 34],\n",
       "       [56, 34]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "take2 = ([[0, 1], [2, 1]],)\n",
    "a[take2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Important! In contrary to slices, fancy indexing always returns a COPY (and not a view) of the array:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[1:3].flags['OWNDATA']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[[1,3]].flags['OWNDATA']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fancy Indexing on Multi Dimensionsnal arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0,  10,  20,  30,  40,  50,  60,  70,  80,  90],\n",
       "       [100, 110, 120, 130, 140, 150, 160, 170, 180, 190],\n",
       "       [200, 210, 220, 230, 240, 250, 260, 270, 280, 290],\n",
       "       [300, 310, 320, 330, 340, 350, 360, 370, 380, 390],\n",
       "       [400, 410, 420, 430, 440, 450, 460, 470, 480, 490]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.arange(50).reshape(5, -1) * 10\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "130"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b[1, 3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "250"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b[2, 5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "260"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b[2, 6]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To use fancy indexing to get items at indexes [1,3] and [2,5] and [2,6], values should be specified for each axis independently:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([130, 250, 260])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b[[1, 2, 2], [3, 5, 6]]"
   ]
  },
  {
   "attachments": {
    "fbae1216-d476-4507-843e-0ab9f425e25d.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bonus: Advanced Fancy Indexing\n",
    "Let's say we want to get the data from rows 1,2,3 and columns 1,2,5,6,8:\n",
    "\n",
    "![image.png](attachment:fbae1216-d476-4507-843e-0ab9f425e25d.png)\n",
    "\n",
    "This will not work:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "ename": "IndexError",
     "evalue": "shape mismatch: indexing arrays could not be broadcast together with shapes (3,) (5,) ",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mIndexError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-17-9f75dede0195>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mb\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m5\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m6\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m8\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mIndexError\u001b[0m: shape mismatch: indexing arrays could not be broadcast together with shapes (3,) (5,) "
     ]
    }
   ],
   "source": [
    "b[[1,2,3], [1,2,5,6,8]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This shortcut works, but it's considered complicated:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[110, 120, 150, 160, 180],\n",
       "       [210, 220, 250, 260, 280],\n",
       "       [310, 320, 350, 360, 380]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b[[1,2,3]][:,[1,2,5,6,8]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Instead it is more common to use `np.ix_`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[1],\n",
       "        [2],\n",
       "        [3]]),\n",
       " array([[1, 2, 5, 6, 8]]))"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.ix_([1,2,3], [1,2,5,6,8])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This result looks strange - but it can be used to fancy select across axes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[110, 120, 150, 160, 180],\n",
       "       [210, 220, 250, 260, 280],\n",
       "       [310, 320, 350, 360, 380]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b[np.ix_([1,2,3], [1,2,5,6,8])]"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}